q-lang-users

[q-lang-users] Q as a Computer Algebra System

[Anthony <ad...@ke...>]

Just a general question...Q is my first experience
with a functional language.  What would it take to
write a Mathematica clone in Q?  

I don't mean a full-Mathematica clone, but something
that would emulate the kernel mode, circa 1988--an
unlimited integer, numeric, graphical, and symbolic
program with an easy syntax.

For example x + 8  will generate internally a
Plus[x,8] production, and 1+x^2+(y+z)^2 generates 

Plus[1, Power[x,2], Power[Plus[y,z],2]]

What I'd like to do is just write a small Q program
that parses a line of input according to the rules of
Mathematica.  No need to evaluate the functions...just
want to build a syntax checker at first.

Or maybe I am dreaming...

Re: [q-lang-users] Q as a Computer Algebra System

[Albert G. <Dr....@t-...>]

dx wrote:
> By the way, is there anyone knows Wm Leler's Bertrand(augmented term rewriting),
> I read the book a long time ago, I am just wondering how close it is to Q.

Sounds interesting. Interesting guy, too. I googled around some but most 
links to actual information and the sources seem to be dead. Does anyone 
have the sources for Bertrand lying around somewhere? I'd like to take a 
look, too.

Albert

-- 
Dr. Albert Gr"af
Dept. of Music-Informatics, University of Mainz, Germany
Email:  Dr....@t-..., ag...@mu...
WWW:    http://www.musikinformatik.uni-mainz.de/ag

Re: [q-lang-users] Q as a Computer Algebra System

[dx <dx...@ac...>]

Hi,

I am attaching the source code that I found.

dex

Albert Graef wrote:
> dx wrote:
>> By the way, is there anyone knows Wm Leler's Bertrand(augmented term rewriting),
>> I read the book a long time ago, I am just wondering how close it is to Q.
> 
> Sounds interesting. Interesting guy, too. I googled around some but most 
> links to actual information and the sources seem to be dead. Does anyone 
> have the sources for Bertrand lying around somewhere? I'd like to take a 
> look, too.
> 
> Albert
> 

[q-lang-users] Q as a Computer Algebra System

[Rob H. <hub...@gm...>]

Hello Anthony,

I too first became interested in 'Q' because of mathematics. I am
fairly new to Q too.

Q is not, in my view, a typical functional language. If you're
interested in learning functional languages, you should also take a
look at some others. It would probably be instructive to try Standard
ML <http://www.smlnj.org/>. There are many other interesting
functional languages. However, I think you will really enjoy using Q.
It's one of the languages that I most enjoy using.

Beware that Q may not always behave quite as you expect at first. For
example, if you enter the simple program consisting of just the
rewrite rule:
    X+X = 2*X;
and the giving Q some expressions to reduce:
    ==> A+A+B
    2*A+B
    ==> A+B+B
    A+B+B
the final response from Q may not be what you expect.

A+B+B, which is (A+B)+B due to the left-associativity of (+), was not
reduced, as this does not match the given rule.
With the additional rule
    Y+X+X = Y+2*X;
you will now get the responses from the Q system
    ==> A+B+B
    A+2*B
    ==> A+A+B+B+C+C+D+D
    2*A+2*B+2*C+2*D

To quote Albert Graef's informative reply to one of my questions:
'Yes, it's surprisingly hard to do apparently basic stuff like this,
because it involves "rewriting modulo AC" (AC =
associativity/commutativity). The conventional way to deal with this
is to transform the original terms into a "sum of products" normal
form and represent that as a list which is lexicographically ordered
according to the involved symbols. It's not really that hard to do but
it indeed involves additional rules on a kind of meta-level, so there
is no straightforward solution with just a few equations.'

I was at first disappointed with Q not being the simple computer
algebra system I hoped it would be. But then that's not what it's
intended to be. Once you get used to it, you find that Q does seem to
do the "right thing". Those involved with developing Q take great care
to keep Q a sensible and consistent language. (See for example the
helpful reply from John Cowan in a discussion
<http://sourceforge.net/mailarchive/message.php?msg_id=19294969> of
type tests, in the lead up to the release of Q7.2)

Not many languages that I know are so well thought out, but I think
that Q is. And Q has fairly comprehensive libraries, together with
comprehensive programming tools, such as the debugger.

When I want to do some maths, I now usually reach for Q. But I tend to
write code for the specific type of mathematical object I'm currently
interested in. I imagine that to write a fairly comprehensive symbolic
computer algebra system would be a job of comparable complexity in any
language, Q, C++, ML, Python, or any other "general purpose" language.

By the way, if anyone does know of a good free / open source symbolic
computer algebra system or programming language, please let me know.
Mathematica is unbelievably expensive, and I don't need anything that
powerful or comprehensive.

I hope these comments (and opinions) are helpful,
Rob.

On 15/08/06, Anthony <ad...@ke...> wrote:
>
> Just a general question...Q is my first experience
> with a functional language.  What would it take to
> write a Mathematica clone in Q?
>
> I don't mean a full-Mathematica clone, but something
> that would emulate the kernel mode, circa 1988--an
> unlimited integer, numeric, graphical, and symbolic
> program with an easy syntax.
>
> For example x + 8  will generate internally a
> Plus[x,8] production, and 1+x^2+(y+z)^2 generates
>
> Plus[1, Power[x,2], Power[Plus[y,z],2]]
>
> What I'd like to do is just write a small Q program
> that parses a line of input according to the rules of
> Mathematica.  No need to evaluate the functions...just
> want to build a syntax checker at first.
>
> Or maybe I am dreaming...

Re: [q-lang-users] Q as a Computer Algebra System

[Kristof B. <kr...@vl...>]

"Rob Hubbard" <hub...@gm...> writes:
> <snip>
>
> By the way, if anyone does know of a good free / open source symbolic
> computer algebra system or programming language, please let me know.
> Mathematica is unbelievably expensive, and I don't need anything that
> powerful or comprehensive.
>

There are several.  Maxima and yacal come to my mind.  The wikipedia
article at http://en.wikipedia.org/wiki/Computer_algebra_system has a
list of propietary and open source algebra systems.  I can't really
say if they are very good, since I haven't used them seriously, but
i.e. when I took a glance at maxima, it seemed quite powerful.

Kristof

Re: [q-lang-users] Q as a Computer Algebra System

[dx <dx...@ac...>]

Hi,

If you want CAS, you can try Maxima or Axiom.

By the way, is there anyone knows Wm Leler's Bertrand(augmented term rewriting),
I read the book a long time ago, I am just wondering how close it is to Q.

Thanks,
dex

Rob Hubbard wrote:
> Hello Anthony,
> 
> I too first became interested in 'Q' because of mathematics. I am
> fairly new to Q too.
> 
> Q is not, in my view, a typical functional language. If you're
> interested in learning functional languages, you should also take a
> look at some others. It would probably be instructive to try Standard
> ML <http://www.smlnj.org/>. There are many other interesting
> functional languages. However, I think you will really enjoy using Q.
> It's one of the languages that I most enjoy using.
> 
> Beware that Q may not always behave quite as you expect at first. For
> example, if you enter the simple program consisting of just the
> rewrite rule:
>     X+X = 2*X;
> and the giving Q some expressions to reduce:
>     ==> A+A+B
>     2*A+B
>     ==> A+B+B
>     A+B+B
> the final response from Q may not be what you expect.
> 
> A+B+B, which is (A+B)+B due to the left-associativity of (+), was not
> reduced, as this does not match the given rule.
> With the additional rule
>     Y+X+X = Y+2*X;
> you will now get the responses from the Q system
>     ==> A+B+B
>     A+2*B
>     ==> A+A+B+B+C+C+D+D
>     2*A+2*B+2*C+2*D
> 
> To quote Albert Graef's informative reply to one of my questions:
> 'Yes, it's surprisingly hard to do apparently basic stuff like this,
> because it involves "rewriting modulo AC" (AC =
> associativity/commutativity). The conventional way to deal with this
> is to transform the original terms into a "sum of products" normal
> form and represent that as a list which is lexicographically ordered
> according to the involved symbols. It's not really that hard to do but
> it indeed involves additional rules on a kind of meta-level, so there
> is no straightforward solution with just a few equations.'
> 
> I was at first disappointed with Q not being the simple computer
> algebra system I hoped it would be. But then that's not what it's
> intended to be. Once you get used to it, you find that Q does seem to
> do the "right thing". Those involved with developing Q take great care
> to keep Q a sensible and consistent language. (See for example the
> helpful reply from John Cowan in a discussion
> <http://sourceforge.net/mailarchive/message.php?msg_id=19294969> of
> type tests, in the lead up to the release of Q7.2)
> 
> Not many languages that I know are so well thought out, but I think
> that Q is. And Q has fairly comprehensive libraries, together with
> comprehensive programming tools, such as the debugger.
> 
> When I want to do some maths, I now usually reach for Q. But I tend to
> write code for the specific type of mathematical object I'm currently
> interested in. I imagine that to write a fairly comprehensive symbolic
> computer algebra system would be a job of comparable complexity in any
> language, Q, C++, ML, Python, or any other "general purpose" language.
> 
> By the way, if anyone does know of a good free / open source symbolic
> computer algebra system or programming language, please let me know.
> Mathematica is unbelievably expensive, and I don't need anything that
> powerful or comprehensive.
> 
> I hope these comments (and opinions) are helpful,
> Rob.
> 
> On 15/08/06, Anthony <ad...@ke...> wrote:
>> Just a general question...Q is my first experience
>> with a functional language.  What would it take to
>> write a Mathematica clone in Q?
>>
>> I don't mean a full-Mathematica clone, but something
>> that would emulate the kernel mode, circa 1988--an
>> unlimited integer, numeric, graphical, and symbolic
>> program with an easy syntax.
>>
>> For example x + 8  will generate internally a
>> Plus[x,8] production, and 1+x^2+(y+z)^2 generates
>>
>> Plus[1, Power[x,2], Power[Plus[y,z],2]]
>>
>> What I'd like to do is just write a small Q program
>> that parses a line of input according to the rules of
>> Mathematica.  No need to evaluate the functions...just
>> want to build a syntax checker at first.
>>
>> Or maybe I am dreaming...
> 
> -------------------------------------------------------------------------
> Using Tomcat but need to do more? Need to support web services, security?
> Get stuff done quickly with pre-integrated technology to make your job easier
> Download IBM WebSphere Application Server v.1.0.1 based on Apache Geronimo
> http://sel.as-us.falkag.net/sel?cmd=lnk&kid=120709&bid=263057&dat=121642
> _______________________________________________
> q-lang-users mailing list
> q-l...@li...
> https://lists.sourceforge.net/lists/listinfo/q-lang-users
> 

Re: [q-lang-users] Q as a Computer Algebra System

[Albert G. <Dr....@t-...>]

Anthony wrote:
> What I'd like to do is just write a small Q program
> that parses a line of input according to the rules of
> Mathematica.  No need to evaluate the functions...just
> want to build a syntax checker at first.

Concerning the parser for the input language, that should be a nice 
opportunity to try Q Yacc+Lex. (The lexical analyzers generated by Q Lex 
are still a bit slow right now, but I'm working on this.)

But, as Rob already explained, building a CAS, even a basic one, is not 
as simple as it might look.

> Or maybe I am dreaming...

Well, I started dreaming about an easy-to-use FP language one day... :)

Cheers,
Albert

-- 
Dr. Albert Gr"af
Dept. of Music-Informatics, University of Mainz, Germany
Email:  Dr....@t-..., ag...@mu...
WWW:    http://www.musikinformatik.uni-mainz.de/ag